Acronym squacufbil Name square-cupofastegia biluna,rotunda of quawros,square atop squobcu Lace cityin approx. ASCII-art ``` x4o x4o x4x x4o ``` Dihedral angles at {3} between tet and trip:   150° at {4} between cube and trip:   arccos(-sqrt[2/3]) = 144.735610° at {3} between tet and tet:   120° at {4} between trip and trip:   arccos(-1/3) = 109.471221° at {4} between cube and cube:   90° at {3} between squobcu and tet:   60° at {4} between squobcu and trip:   arccos[1/sqrt(3)] = 54.735610° at {4} between cube and squobcu:   45° Confer more general: n-cufbil   related segmentochora: {8} || cube   related CRFs: quawros   general polytopal classes: bistratic lace towers

Incidence matrix according to Dynkin symbol

```{4} || squobcu   → height = 1/sqrt(2) = 0.707107

4 * * * | 2 1 2 1 0 0 0 0 0 0 | 1 2 2 2 2 1 2 0 0 0 0 0 0 | 1 1 2 2 1 1 0  top (A)
* 4 * * | 0 1 0 0 2 2 0 0 0 0 | 0 2 0 0 2 0 0 1 2 1 0 0 0 | 1 0 2 0 1 0 1  bottom (A)
* * 8 * | 0 0 1 0 0 1 1 1 1 0 | 0 0 1 0 1 1 1 0 1 1 1 1 0 | 0 0 1 1 1 1 1  bottom (B)
* * * 4 | 0 0 0 1 0 0 0 0 2 2 | 0 0 0 2 0 0 2 0 0 0 2 1 1 | 0 1 0 2 0 1 1  bottom (A)
--------+---------------------+---------------------------+--------------
2 0 0 0 | 4 * * * * * * * * * | 1 1 1 1 0 0 0 0 0 0 0 0 0 | 1 1 1 1 0 0 0
1 1 0 0 | * 4 * * * * * * * * | 0 2 0 0 2 0 0 0 0 0 0 0 0 | 1 0 2 0 1 0 0
1 0 1 0 | * * 8 * * * * * * * | 0 0 1 0 1 1 1 0 0 0 0 0 0 | 0 0 1 1 1 1 0
1 0 0 1 | * * * 4 * * * * * * | 0 0 0 2 0 0 2 0 0 0 0 0 0 | 0 1 0 2 0 1 0
0 2 0 0 | * * * * 4 * * * * * | 0 1 0 0 0 0 0 1 1 0 0 0 0 | 1 0 1 0 0 0 1
0 1 1 0 | * * * * * 8 * * * * | 0 0 0 0 1 0 0 0 1 1 0 0 0 | 0 0 1 0 1 0 1
0 0 2 0 | * * * * * * 4 * * * | 0 0 1 0 0 0 0 0 1 0 1 0 0 | 0 0 1 1 0 0 1  para
0 0 2 0 | * * * * * * * 4 * * | 0 0 0 0 0 1 0 0 0 1 0 1 0 | 0 0 0 0 1 1 1  obligue
0 0 1 1 | * * * * * * * * 8 * | 0 0 0 0 0 0 1 0 0 0 1 1 0 | 0 0 0 1 0 1 1
0 0 0 2 | * * * * * * * * * 4 | 0 0 0 1 0 0 0 0 0 0 1 0 1 | 0 1 0 1 0 0 1
--------+---------------------+---------------------------+--------------
4 0 0 0 | 4 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * | 1 1 0 0 0 0 0
2 2 0 0 | 1 2 0 0 1 0 0 0 0 0 | * 4 * * * * * * * * * * * | 1 0 1 0 0 0 0
2 0 2 0 | 1 0 2 0 0 0 1 0 0 0 | * * 4 * * * * * * * * * * | 0 0 1 1 0 0 0
2 0 0 2 | 1 0 0 2 0 0 0 0 0 1 | * * * 4 * * * * * * * * * | 0 1 0 1 0 0 0
1 1 1 0 | 0 1 1 0 0 1 0 0 0 0 | * * * * 8 * * * * * * * * | 0 0 1 0 1 0 0
1 0 2 0 | 0 0 2 0 0 0 0 1 0 0 | * * * * * 4 * * * * * * * | 0 0 0 0 1 1 0
1 0 1 1 | 0 0 1 1 0 0 0 0 1 0 | * * * * * * 8 * * * * * * | 0 0 0 1 0 1 0
0 4 0 0 | 0 0 0 0 4 0 0 0 0 0 | * * * * * * * 1 * * * * * | 1 0 0 0 0 0 1
0 2 2 0 | 0 0 0 0 1 2 1 0 0 0 | * * * * * * * * 4 * * * * | 0 0 1 0 0 0 1
0 1 2 0 | 0 0 0 0 0 2 0 1 0 0 | * * * * * * * * * 4 * * * | 0 0 0 0 1 0 1
0 0 2 2 | 0 0 0 0 0 0 1 0 2 1 | * * * * * * * * * * 4 * * | 0 0 0 1 0 0 1
0 0 2 1 | 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * 4 * | 0 0 0 0 0 1 1
0 0 0 4 | 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * 1 | 0 1 0 0 0 0 1
--------+---------------------+---------------------------+--------------
4 4 0 0 | 4 4 0 0 4 0 0 0 0 0 | 1 4 0 0 0 0 0 1 0 0 0 0 0 | 1 * * * * * *  cube
4 0 0 4 | 4 0 0 4 0 0 0 0 0 4 | 1 0 0 4 0 0 0 0 0 0 0 0 1 | * 1 * * * * *  cube
2 2 2 0 | 1 2 2 0 1 2 1 0 0 0 | 0 1 1 0 2 0 0 0 1 0 0 0 0 | * * 4 * * * *  trip
2 0 2 2 | 1 0 2 2 0 0 1 0 2 1 | 0 0 1 1 0 0 2 0 0 0 1 0 0 | * * * 4 * * *  trip
1 1 2 0 | 0 1 2 0 0 2 0 1 0 0 | 0 0 0 0 2 1 0 0 0 1 0 0 0 | * * * * 4 * *  tet
1 0 2 1 | 0 0 2 1 0 0 0 1 2 0 | 0 0 0 0 0 1 2 0 0 0 0 1 0 | * * * * * 4 *  tet
0 4 8 4 | 0 0 0 0 4 8 4 4 8 4 | 0 0 0 0 0 0 0 1 4 4 4 4 1 | * * * * * * 1  squobcu
```

```x(xx)x4o(ox)o&#xt   → height(1,2) = height(2,3) = 1/sqrt(2) = 0.707107
({4} || pseudo squacu || {4})

o(..).4o(..).     | 4 * * * | 2 1 2 0 0 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0
.(o.).4.(o.).     | * 4 * * | 0 1 0 2 2 1 0 0 0 0 | 0 2 0 0 2 1 2 1 2 2 0 0 0 | 1 0 2 1 1 2 1
.(.o).4.(.o).     | * * 8 * | 0 0 1 0 1 0 1 1 1 0 | 0 0 1 1 1 0 1 1 0 1 1 1 0 | 0 1 1 1 0 1 1
.(..)o4.(..)o     | * * * 4 | 0 0 0 0 0 1 0 0 2 2 | 0 0 0 0 0 0 0 0 2 2 2 1 1 | 0 1 0 0 1 2 1
------------------+---------+---------------------+---------------------------+--------------
x(..). .(..).     | 2 0 0 0 | 4 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0
o(o.).4o(o.).&#x  | 1 1 0 0 | * 4 * * * * * * * * | 0 2 0 0 2 0 0 0 0 0 0 0 0 | 1 0 2 1 0 0 0
o(.o).4o(.o).&#x  | 1 0 1 0 | * * 8 * * * * * * * | 0 0 1 1 1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0
.(x.). .(..).     | 0 2 0 0 | * * * 4 * * * * * * | 0 1 0 0 0 1 1 0 1 0 0 0 0 | 1 0 1 0 1 1 0
.(oo).4.(oo).&#x  | 0 1 1 0 | * * * * 8 * * * * * | 0 0 0 0 1 0 1 1 0 1 0 0 0 | 0 0 1 1 0 1 1
.(o.)o4.(o.)o&#x  | 0 1 0 1 | * * * * * 4 * * * * | 0 0 0 0 0 0 0 0 2 2 0 0 0 | 0 0 0 0 1 2 1
.(.x). .(..).     | 0 0 2 0 | * * * * * * 4 * * * | 0 0 1 0 0 0 1 0 0 0 1 0 0 | 0 1 1 0 0 1 0
.(..). .(.x).     | 0 0 2 0 | * * * * * * * 4 * * | 0 0 0 1 0 0 0 1 0 0 0 1 0 | 0 1 0 1 0 0 1
.(.o)o4.(.o)o&#x  | 0 0 1 1 | * * * * * * * * 8 * | 0 0 0 0 0 0 0 0 0 1 1 1 0 | 0 1 0 0 0 1 1
.(..)x .(..).     | 0 0 0 2 | * * * * * * * * * 4 | 0 0 0 0 0 0 0 0 1 0 1 0 1 | 0 1 0 0 1 1 0
------------------+---------+---------------------+---------------------------+--------------
x(..).4o(..).     | 4 0 0 0 | 4 0 0 0 0 0 0 0 0 0 | 1 * * * * * * * * * * * * | 1 1 0 0 0 0 0
x(x.). .(..).&#x  | 2 2 0 0 | 1 2 0 1 0 0 0 0 0 0 | * 4 * * * * * * * * * * * | 1 0 1 0 0 0 0
x(.x). .(..).&#x  | 2 0 2 0 | 1 0 2 0 0 0 1 0 0 0 | * * 4 * * * * * * * * * * | 0 1 1 0 0 0 0
.(..). o(.x).&#x  | 1 0 2 0 | 0 0 2 0 0 0 0 1 0 0 | * * * 4 * * * * * * * * * | 0 1 0 1 0 0 0
o(oo).4o(oo).&#x  | 1 1 1 0 | 0 1 1 0 1 0 0 0 0 0 | * * * * 8 * * * * * * * * | 0 0 1 1 0 0 0
.(x.).4.(o.).     | 0 4 0 0 | 0 0 0 4 0 0 0 0 0 0 | * * * * * 1 * * * * * * * | 1 0 0 0 1 0 0
.(xx). .(..).&#x  | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 0 | * * * * * * 4 * * * * * * | 0 0 1 0 0 1 0
.(..). .(ox).&#x  | 0 1 2 0 | 0 0 0 0 2 0 0 1 0 0 | * * * * * * * 4 * * * * * | 0 0 0 1 0 0 1
.(x.)x .(..).&#x  | 0 2 0 2 | 0 0 0 1 0 2 0 0 0 1 | * * * * * * * * 4 * * * * | 0 0 0 0 1 1 0
.(oo)o4.(oo)o&#x  | 0 1 1 1 | 0 0 0 0 1 1 0 0 1 0 | * * * * * * * * * 8 * * * | 0 0 0 0 0 1 1
.(.x)x .(..).&#x  | 0 0 2 2 | 0 0 0 0 0 0 1 0 2 1 | * * * * * * * * * * 4 * * | 0 1 0 0 0 1 0
.(..). .(.x)o&#x  | 0 0 2 1 | 0 0 0 0 0 0 0 1 2 0 | * * * * * * * * * * * 4 * | 0 1 0 0 0 0 1
.(..)x4.(..)o     | 0 0 0 4 | 0 0 0 0 0 0 0 0 0 4 | * * * * * * * * * * * * 1 | 0 1 0 0 1 0 0
------------------+---------+---------------------+---------------------------+--------------
x(x.).4o(o.).&#x  ♦ 4 4 0 0 | 4 4 0 4 0 0 0 0 0 0 | 1 4 0 0 0 1 0 0 0 0 0 0 0 | 1 * * * * * *
x(.x)x4o(.x)x&#xt ♦ 4 0 8 4 | 4 0 8 0 0 0 4 4 8 4 | 1 0 4 4 0 0 0 0 0 0 4 4 1 | * 1 * * * * *
x(xx). .(..).&#x  ♦ 2 2 2 0 | 1 2 2 1 2 0 1 0 0 0 | 0 1 1 0 2 0 1 0 0 0 0 0 0 | * * 4 * * * *
.(..). o(ox).&#x  ♦ 1 1 2 0 | 0 1 2 0 2 0 0 1 0 0 | 0 0 0 1 2 0 0 1 0 0 0 0 0 | * * * 4 * * *
.(x.)x4.(o.)o&#x  ♦ 0 4 0 4 | 0 0 0 4 0 4 0 0 0 4 | 0 0 0 0 0 1 0 0 4 0 0 0 1 | * * * * 1 * *
.(xx)x .(..).&#x  ♦ 0 2 2 2 | 0 0 0 1 2 2 1 0 2 1 | 0 0 0 0 0 0 1 0 1 2 1 0 0 | * * * * * 4 *
.(..). .(ox)o&#x  ♦ 0 1 2 1 | 0 0 0 0 2 1 0 1 2 0 | 0 0 0 0 0 0 0 1 0 2 0 1 0 | * * * * * * 4
```
```or
o(..).4o(..).     & | 8 * * | 2 1  2 0 0 0 0 | 1 2 2 1  2 0 0 0 | 1 1 2 1
.(o.).4.(o.).       | * 4 * | 0 2  0 2 2 0 0 | 0 4 0 0  4 1 2 1 | 2 0 4 2
.(.o).4.(.o).       | * * 8 | 0 0  2 0 1 1 1 | 0 0 2 2  2 0 1 1 | 0 1 2 2
--------------------+-------+----------------+------------------+--------
x(..). .(..).     & | 2 0 0 | 8 *  * * * * * | 1 1 1 0  0 0 0 0 | 1 1 1 0
o(o.).4o(o.).&#x  & | 1 1 0 | * 8  * * * * * | 0 2 0 0  2 0 0 0 | 1 0 2 1
o(.o).4o(.o).&#x  & | 1 0 1 | * * 16 * * * * | 0 0 1 1  1 0 0 0 | 0 1 1 1
.(x.). .(..).       | 0 2 0 | * *  * 4 * * * | 0 2 0 0  0 1 1 0 | 2 0 2 0
.(oo).4.(oo).&#x    | 0 1 1 | * *  * * 8 * * | 0 0 0 0  2 0 1 1 | 0 0 2 2
.(.x). .(..).       | 0 0 2 | * *  * * * 4 * | 0 0 2 0  0 0 1 0 | 0 1 2 0
.(..). .(.x).       | 0 0 2 | * *  * * * * 4 | 0 0 0 2  0 0 0 1 | 0 1 0 2
--------------------+-------+----------------+------------------+--------
x(..).4o(..).     & | 4 0 0 | 4 0  0 0 0 0 0 | 2 * * *  * * * * | 1 1 0 0
x(x.). .(..).&#x  & | 2 2 0 | 1 2  0 1 0 0 0 | * 8 * *  * * * * | 1 0 1 0
x(.x). .(..).&#x  & | 2 0 2 | 1 0  2 0 0 1 0 | * * 8 *  * * * * | 0 1 1 0
.(..). o(.x).&#x  & | 1 0 2 | 0 0  2 0 0 0 1 | * * * 8  * * * * | 0 1 0 1
o(oo).4o(oo).&#x  & | 1 1 1 | 0 1  1 0 1 0 0 | * * * * 16 * * * | 0 0 1 1
.(x.).4.(o.).       | 0 4 0 | 0 0  0 4 0 0 0 | * * * *  * 1 * * | 2 0 0 0
.(xx). .(..).&#x    | 0 2 2 | 0 0  0 1 2 1 0 | * * * *  * * 4 * | 0 0 2 0
.(..). .(ox).&#x    | 0 1 2 | 0 0  0 0 2 0 1 | * * * *  * * * 4 | 0 0 0 2
--------------------+-------+----------------+------------------+--------
x(x.).4o(o.).&#x  & ♦ 4 4 0 | 4 4  0 4 0 0 0 | 1 4 0 0  0 1 0 0 | 2 * * *
x(.x)x4o(.x)x&#xt   ♦ 8 0 8 | 8 0 16 0 0 4 4 | 2 0 8 8  0 0 0 0 | * 1 * *
x(xx). .(..).&#x  & ♦ 2 2 2 | 1 2  2 1 2 1 0 | 0 1 1 0  2 0 1 0 | * * 8 *
.(..). o(ox).&#x  & ♦ 1 1 2 | 0 1  2 0 2 0 1 | 0 0 0 1  2 0 0 1 | * * * 8
```